Question 3.A consumer has a locally nonsatiating preference represented by a utility function u(x, y).Assume that u is continuous at all (x, y) where x20 and y 2 0. This consumer's expenditure function is given by1[2(p1Pzu)} –PiР2 ifP2иE(p1, P2, u) =1PiifP2Find this consumer's utility function u(x, y) and the missing formula for E(p1, p2, u).

Utility function is a mathematical representation to quantify a consumer's alternatives over…

Question 3. A consumer has a locally nonsatiating preference represented by a utility function u(x, y). Assume that u is continuous at all (x, y) where x≥ 0 and y≥0. This consumer's expenditure function is given by P1 [2(P1 P2u) = − 1 -P2 if E(P1, P2, u). P2 u ? P1 1 if S P2 и Find this consumer's utility function u(x, y) and the missing formula for E(p1, p2, u).

Question 3. A consumer has a locally nonsatiating preference represented by a utility function u(x, y). Assume that u is continuous at all (x, y) where x≥ 0 and y≥0. This consumer's expenditure function is given by P1 [2(P1 P2u) = − 1 -P2 if E(P1, P2, u). P2 u ? P1 1 if S P2 и Find this consumer's utility function u(x, y) and the missing formula for E(p1, p2, u).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…
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4please answer part a and b of quesrion #1
solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)
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. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.
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